The chromatic number, $\chi(G)$ of a graph $G$ is the minimum number of colours used in a proper colouring of $G$. In an improper colouring, an edge $uv$ is bad if the colours assigned to the end vertices of the edge is ...

A subset $S$ of vertices in a graph $G=(V,E)$ is $2$-independent if everyvertex of $S$ has at most one neighbor in $S.$ The $2$-independence numberis the maximum cardinality of a $2$-independent set of $G.$ In this paper,we ...

For a simple, undirected, connected graph $G$($V,E$), a function $f : V(G) \rightarrow \lbrace 0, 1, 2 \rbrace$ which satisfies the following conditions is called a quasi-total Roman dominating function (QTRDF) of $G$ with ...

In this short note, we disprove the conjecture of Jafari Rad and Volkmannthat every $\gamma $-vertex critical graph is $\gamma _{R}$-vertex critical,where $\gamma (G)$ and $\gamma _{R}(G)$ stand for the domination number ...

The energy of a graph G, denoted by Ε(G), is defined as the sum of the absolute values of all eigenvalues of G. In this paper, lower and upper bounds for energy in some of the graphs are established, in terms of graph ...

To extract some more information from the constructions of matroids that arise from new operations, computing the Tutte polynomial, plays an important role. In this paper, we consider applying three operations of splitting, ...

In this paper, we initiate the study of total outer-convex domination as a new variant of graph domination and we show the close relationship that exists between this novel parameter and other domination parameters of a ...

If $A(G)$ and $D(G)$ are respectively the adjacency matrix and the diagonal matrix of vertex degrees of a connected graph $G$, the generalized adjacency matrix $A_{\alpha}(G)$ is defined as $A_{\alpha}(G)=\alpha ...

A signed graph is an ordered pair $\Sigma=(G,\sigma),$ where $G=(V,E)$ is the underlying graph of $\Sigma$ with a signature function $\sigma:E\rightarrow \{1,-1\}$.In this article, we define the $n^{th}$ power of a signed ...

In this paper, we present a second-order corrector infeasibleinterior-point method for linear optimization in a largeneighborhood of the central path. The innovation of our method is tocalculate the predictor directions ...

Let $k\ge 1$ be an integer. A { weak signed Roman $k$-dominating function} on a graph $G$ isa function  $f:V (G)\longrightarrow \{-1, 1, 2\}$ such that $\sum_{u\in N[v]}f(u)\ge k$ for every$v\in V(G)$, where $N[v]$ is the ...

For a given graph $ G $, its $\mathscr{P}$-energy is the sum of the absolute values of the eigenvalues of the  $\mathscr{P}$-matrix of $ G $. In this article, we explore the $\mathscr{P}$-energy of generalized Petersen ...